Rigging 2D elephant trunk corrupts the mesh
A tube with an armature as its spine which used Bind with automatic weights.  Image above.




Back up your current work with file save
Create a new quick cylinder with loopcuts say 20. Scale to your tastes and elephant trunk shape.  Keep the cylinder in straight line.  
Create a new armature with 20 bones. Keep the original straight shape.
The more loop cuts in the cylinder mesh, with more bones in the armature, will allow a smoother movement.
Move the armature to be located in the cylinder. Make sure trunk is reasonable tight fit to armature. A tube with no fancy shape is fine because the tube can be changed later after binding to armature.  The learning experience will be better.
The above steps will take 8 minutes with practice
Ensure the placement by examining from different angles
Bind Trunk to Armature with automatic weights
You may choose reserve frame 1 for the straight armature shape and insert keyframes for all bones.
Move to some other frame say frame 8
Test the binding by rotating bones of the armature in pose mode. Insert keyframes.
You can create a shape key for the cylinder mesh if you like
You can shape the trunk with more lifelike shape
These above steps are an improvement. If you wind the bones in too tight of a spiral you might not like the results. Bad results such as this can be true of any simple model for Blender Beginners.
Delete all previous work when satisfied.  Your previous work has some new user problems which can be discarded.  A fresh start can be good.
Be aware of the Spline IK constraint which allows a smooth curve to control the armature and may save time once its mastered